Minyan Mailbag: Derivatives Mis-pricing

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Editor's Note: Minyanville is a community of people who share an interest in fiscal literacy. As perspective is an important aspect of our daily routine, we share this exchange with hopes that it adds balance to your process.

Professor Succo,

Credit risk can, in essence, be decomposed into two (closely-related and -correlated) categories, credit deterioration and default risk. It might be helpful to think of the former as the price of medical insurance and the latter as the price of life insurance. In a CDS contract periodic payments are made from the purchaser of protection to the seller until either default occurs or the swap expires.

In many ways they're also similar to deep OTM put options, indeed some people gamma hedge the CDS in the equity based on the theory that the price of the equity is related to distance to default (OTM equity puts will at times also be purchased as default protection instead of a CDS).

There are two ways to settle a CDS: through physical delivery and through cash. In a cash settled CDS at default the protection buyer will receive X dollars (a specified amount, usually par, minus the recovery value of the reference bond) from the seller. Physical settlement is even simpler; the purchaser of protection will simply put the bond to the seller in exchange for par.

The existence of a reasonably liquid market for credit default swaps is possible because a risky bond can, theoretically, be decomposed into three distinct financial instruments: an interest rate swap, a floating rate note and a CDS. For example:

A bond has a tenor of five years, it is purchased at par value (for a cash flow of -B) at T0. It pays an annual coupon (C) at T1 through to maturity (T5) and will also return the principal (cash flow B) at T5. To simplify let's say the credit can only default at T5, at which point the owner of the bond will either receive P+C or, in the case of default, 0 . To isolate the default option we separate the cash flows of the bond transaction into: the coupons at T1 through T5 in the case of no default; the price of the bond -B at T0 and the return of B at T5 in the case of no default; and -B and -C at T5 if a default occurs. Now we have three distinct bundles of cash flow, but to sell them to investors we need to convert them in marketable instruments. To do this we add and subtract cash flows, we can do this as much as we want as long as the net cash flows of all the instruments are equal to those of the original bond.

Firstly we can convert the original coupon payments into a fixed receiver swap. We do this by adding a default-free variable rate cash flow (V) to the coupon flows. However, due to the default risk of the bond the interest rate on a fixed receiver swap is lower than the coupon rate on the bond at T0 (the spread over the swap rate (S) is C-S at T0. Let this difference be D. Obviously we can re-arrange this equation so that C-D=S). So if we subtract cash flow D from C we have an instrument which, from T1 to T5, receives V and pays S: a standard receiver swap, a very marketable instrument. Now we have two extra cash flows, V and D, which we need to put somewhere.

The natural place to put V is into the second bundle of cash flows from the original bond: -B at T0 and +B at T5. Now we have an instrument with cash flows of -B at T0, V at T1 though T4 and V+B at T5. We've created a floating rate note, another very marketable instrument.

We're left with the third bundle of cash flows: this time potential -B and -C at T5 contingent on default, and D. So this time we have an instrument which receives D at T1 through T5, but pays -B and -C at T5 if default occurs. This is a credit default swap.

So we've taken the cash flow of a bond and turned it into three very different instruments. Having done this we can now see how a broker-dealer can price and hedge (and hence make a market in) a CDS (and, interestingly, how to create synthetic assets; useful either for arbitrage purposes or because they don't exist). Obviously this is highly simplified and the real world introduces a number of complications, but that's the basic theory. A few of the complications:

• Bonds of the same maturity as the CDS may not even exist, which makes pricing more complex and means that swap counterparties are over exposed to credit risk versus the market risk of the bond. Even when a bond of the same tenor is available sometimes the market will dry-up (in 1998, for example, cash bond dealers totally stopped quoting prices on many corporates).

• There are differences in the taxation of corporate paper and credit default swaps.

• In a CDS settled through physical delivery a basket of bonds are deliverable, creating an embedded delivery option.

• Then there are legal problems with both defaults (something we saw back in 01/02) and restructuring and how these affect the legal status of a CDS, a problem made larger by the somewhat heterogeneous terms of CDSs.

• The hedges of the purchaser and seller of a CDS are asymmetric.

The seller of protection needs to borrow money, usually at LIBOR, to purchase a bond paying over LIBOR. The purchaser of protection needs to borrow the bond in the repo market, getting less than LIBOR, and then sell it in the debt market paying the buyer more than LIBOR. My understanding of what the NY Fed is looking at is that their primary concern is the assignment and confirmation problems in the CDS market. If I want to buy X bonds of Widget Inc and there's a matching axe the trade will get confirmed by the back offices of both sides of the trade that same day. If I want to enter into a CDS on Widget Inc debt the trade might not get confirmed for a month (sometimes more).

There are two problems here: firstly, and this is potentially a big one, for a broker-dealer to do business with another firm (a hedge fund for example) it needs to understand the risk it has on so that it can give them a line. If the trades are not confirmed they, in effect, do not exist, so the risk level may be significantly understated. Secondly, there could be a trade error and someone might fail on payment. Speaking to people on the sell-side, these issues are getting worked out (through the DTCC, Swapswire etc), but I think the NY Fed (quite rightly, in my opinion) will ask the broker-dealers to improve settlement and confirmation times and perhaps they'll also ask them to be more careful on giving credit lines to hedge funds (something the Fed has talked about publicly). There's already been a lot of work done, primarily by the ISDA, on standardizing contracts, but this could also be improved further as the heterogeneous nature of CDSs can create problems in high-stress conditions.

All-in-all it doesn't look like another 1998 type scenario to me at the moment, but I could be wrong (we have historically had financial "accidents" during monetary tightening cycles!).

Many thanks,

Minyan Michael Scurfield

Minyan Michael,

The NY Fed as you state, and as I stated previously, will predominantly be looking at settlement issues. You state that they have come a long way and there shouldn't be major problems. I agree, and this is the result of years of clearing other types of derivatives and learning how to avoid these types of risks. But they are the easiest type to minimize.

Thank you for graciously de-structuring the flows of CDS; I am quite familiar with them, but did not go into them as I felt they might distract the general community from my primary point (now Minyans can save your detailed response and study it).

Derivatives in general have a serious problem, one of pricing. In essence, derivatives are being carried on the books of dealers at prices that can't clear the market. There are billions of dollars in profits already taken that should be reserved for contingent events, like early unwinds. They may have been initially priced correctly when clearing the market, but then when profits are needed, they are remarked to take much of the present value profits left. If several large institutions remarked their books to a proper present value price, a few would have to realize huge write-downs. This is a little like the scam where companies have been stealing from their pension plans to make earnings estimates.

The derivatives themselves are not the problem. I think derivatives, including CDS, are good products with useful risk altering functions. The problem is human in nature, the tendency to take profits now rather than be prudent.

We cannot state that this is not a 1998 magnitude problem or even worse. The fact is we do not know the magnitude of the miss-markings because we are not privy to them. Fannie Mae (FNM) is one of the world's largest users of derivatives and was found to "hide" derivative losses just by an allowed convolution of their financial statements. And now they have closed their books entirely to the public. That is a good indication that there is a problem.

Independent verification of derivative pricing, especially to FNM's counter-parties is needed before the market lets us know.

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